Theta_Sigma: By all means, I have a mish-mash of 1st, 2nd, 3rd (most the the Dalek War set), 4th, 6th, 7th, and obvious continuation series', but I'm always open to suggestions in case there is something I may have missed, or forgotten about.
StingingVelvet: In that Dalek War set is one of my favorite Pertwee stories, Frontier in Space. If you liked that try the Peladon stories, or Death to the Daleks. I like a lot of Pertwee, for whatever reason... seems more sci-fi to me.
Caves of Androzani and Seeds of Doom are two of my favorite Doctor Who stories, if you don't have them yet. I think McCoy's final season is surprisingly good compared to the 5 years of mostly shite that came before it. Ghost Light and Curse of Fenric are especially entertaining for me. Ghost Light really requires a lot of thought to understand, though.
And my favorite Doctor is Patrick Troughton, I love that old Twilight Zone style 60's sci-fi. Every DVD of his is worth getting really, except maybe The Mind Robber.
That is a great story, most of Pertwee's run is just absolutely spectacular, plus he was essentially the "James Bond" Doctor for all intense purposes. There was so much about his time with UNIT that was a joy, and Nick Courtney was always awesome. I can see why you would feel it more sci-fi.
While I am not overly fond of Peter Davison's run (stories wise), there are a few serials I really do like, and Caves of Androzani is most certainly one of them. I cannot remember if I've ever seen Seeds of Doom, but I will most certainly look it up and I don't have it I'll grab a copy. I love McCoy's Doctor, especially with his charisma and darker nature, for all the grief I have given JNT, he did strike a lot of home runs with the 7th Doctor. I agree with you with exception of Trial of a Time Lord, I thought the story was rather good, and I thought Colin Baker did a fantastic job in them. Ghost Light and Curse of Fenric I do have and I agree those are really good episodes. You really see such a wonderful dynamic between Ace and the Doctor, almost a father/daughter situation, and so much more enjoyable to watch than the Doctor and Susan. Well Ghost Light was originally supposed to be Lungbarrow (prior to the novel) if I'm not mistaken, which was going to be a complex story in, and of itself.
While he is not my absolute favourite, Troughton is one of my favourites, and one of the first attempts at making a complex and "darker" Doctor. His portrayal was absolutely a delight, and I always love watching any episode that features him, even post tenure. I agree pretty much every DVD of his run is worth acquiring, I don't have many, but I do have the War Games around here somewhere, which was one of my favourites.
BoxOfSnoo: Oh and I hope they don't regenerate into a female doctor, because I'm positive it would be just a gimmick. Totally unnecessary baggage for the story.
StingingVelvet: Caves of Androzani and Seeds of Doom are two of my favorite Doctor Who stories, if you don't have them yet.
BoxOfSnoo: Ahh, I remember Seeds of Doom. I enjoyed that... and I seem to remember enjoying "Timelash" quite a bit.
I am sure that likely won't happen, and that isn't a slight on a woman in the role, but the canon not being taken into account, it would cause too much of a fan backlash (enough that it would be problematic) that they would probably not want to risk destroying the popularity of the show. I think if they REALLY want to have a female Time Lord in the show they should either bring back Jenny, Romana, Susan, or even possibly release the Time Lords from the lock and they open up the flood gates to a variety of new characters. Mind you this is just my opinion, and by no means should or should not be done. :)